It has been stated by Lucian in An Elite Meet and Greet! that when a Trainer wins their respective region's Conference Tournament, they can participate in the Champion League, fighting the four members of that region's Elite Four, and then possibly the Champion as well. It has also been shown that an Elite Four member can challenge the Champion and obtain the title from him or her in battle.

The Hoenn Elite Four, consisting of Sidney, Phoebe, Glacia and Drake, made an appearance in the Ruby & Sapphire chapter, helping to find and catch the legendary titans in order to contain the massive surge of energy created by the clash of Kyogre and Groudon alongside Steven and Wallace, their two regional Champions. It is also during the Hoenn Elite Four's appearance that the challenge of the Elite Four and Champion was mentioned as having replaced a knockout tournament to determine the best Trainer in the region.

The Unova Elite Four first appeared in the Black & White chapter as Black cites them during his daily pledge. However, they haven't appeared to the main characters as a group yet. Besides Caitlin, who already appeared in the Platinum chapter, Grimsley meets Black, Shauntal meets White, and Marshal meets both on different occasions. All four converge for the duration of the Unova League tournament that would have determined the Trainer that would challenge them.

The first Kalos Elite Four member to appear is Malva, who appeared in person in X & Y chapter. Drasna, Wikstrom, and Siebold were mentioned by Diantha during her conversation with Gurkinn and Korrina. Siebold later appeared in the Lost Hotel, cooking a meal for X and Y's friends, as a way of apologizing for his lack of participation against Team Flare. Wikstrom and Drasna later appeared in person, assissting
X and Y's group in their quest to stop Team Flare. Drasna gave them information about Zygarde and Wikstrom used his Probopass to guide them to Team Flare's hideout.

In the Pokémon Zensho manga

The Kanto Elite Four members appeared in Indigo Plateau, where all of them were defeated by Satoshi, allowing him to face the Champion, Shigeru.

Trivia

In the Kanto-based games, every Elite Four member has at least one Pokémon not of their specialty type during the first battle.

The Kalos Elite Four members are the only ones that don't have higher level Pokémon in future rematches with them in any game.

Additionally, they are the only ones who use just four Pokémon in rematches with them. All other Elite Four members use either five or six Pokémon during rematches.

Prior to Generation V, the Elite Four typically progressed in level with their Pokémon in the games. Starting in Generation V, all members of the Elite Four (except in remakes) use Pokémon of the same levels, as they can be challenged in any order.

The Sinnoh Elite Four and Generation I Elite Four are the only Elite Four of which all members have appeared in the anime.